Tensor decomposition is now being used for data analysis, information compression, and knowledge recovery. However, the mathematical property of tensor decomposition is not yet fully clarified because it is one of singular learning machines. In this paper, we give the upper bound of its real log canonical threshold (RLCT) of the tensor decomposition by using an algebraic geometrical method and derive its Bayesian generalization error theoretically. We also give considerations about its mathematical property through numerical experiments.

翻译：张量分解现在被用于数据分析、信息压缩和知识恢复。然而，由于它是一种奇异的学习机器之一，因此张量分解的数学性质尚未完全阐明。本文通过代数几何方法给出了张量分解的实对数典范阈(Real Log Canonical Threshold, RLCT)上界，并从理论上推导了其贝叶斯广义误差。我们还通过数值实验探讨了其数学性质。